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Calculus Examples
Step 1
Differentiate using the Product Rule which states that is where and .
Step 2
Step 2.1
By the Sum Rule, the derivative of with respect to is .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 2.3
Since is constant with respect to , the derivative of with respect to is .
Step 2.4
Differentiate using the Power Rule which states that is where .
Step 2.5
Multiply by .
Step 2.6
By the Sum Rule, the derivative of with respect to is .
Step 2.7
Apply basic rules of exponents.
Step 2.7.1
Rewrite as .
Step 2.7.2
Multiply the exponents in .
Step 2.7.2.1
Apply the power rule and multiply exponents, .
Step 2.7.2.2
Multiply by .
Step 2.8
Differentiate using the Power Rule which states that is where .
Step 2.9
Since is constant with respect to , the derivative of with respect to is .
Step 2.10
Apply basic rules of exponents.
Step 2.10.1
Rewrite as .
Step 2.10.2
Multiply the exponents in .
Step 2.10.2.1
Apply the power rule and multiply exponents, .
Step 2.10.2.2
Multiply by .
Step 2.11
Differentiate using the Power Rule which states that is where .
Step 2.12
Multiply by .
Step 3
Step 3.1
Rewrite the expression using the negative exponent rule .
Step 3.2
Rewrite the expression using the negative exponent rule .
Step 3.3
Combine terms.
Step 3.3.1
Combine and .
Step 3.3.2
Move the negative in front of the fraction.
Step 3.3.3
Combine and .
Step 3.4
Reorder terms.
Step 3.5
Simplify each term.
Step 3.5.1
Expand using the FOIL Method.
Step 3.5.1.1
Apply the distributive property.
Step 3.5.1.2
Apply the distributive property.
Step 3.5.1.3
Apply the distributive property.
Step 3.5.2
Simplify and combine like terms.
Step 3.5.2.1
Simplify each term.
Step 3.5.2.1.1
Multiply by .
Step 3.5.2.1.2
Multiply by .
Step 3.5.2.1.3
Cancel the common factor of .
Step 3.5.2.1.3.1
Factor out of .
Step 3.5.2.1.3.2
Cancel the common factor.
Step 3.5.2.1.3.3
Rewrite the expression.
Step 3.5.2.1.4
Cancel the common factor of .
Step 3.5.2.1.4.1
Move the leading negative in into the numerator.
Step 3.5.2.1.4.2
Factor out of .
Step 3.5.2.1.4.3
Factor out of .
Step 3.5.2.1.4.4
Cancel the common factor.
Step 3.5.2.1.4.5
Rewrite the expression.
Step 3.5.2.1.5
Combine and .
Step 3.5.2.1.6
Multiply by .
Step 3.5.2.1.7
Move the negative in front of the fraction.
Step 3.5.2.2
Combine the numerators over the common denominator.
Step 3.5.2.3
Subtract from .
Step 3.5.3
Move the negative in front of the fraction.
Step 3.5.4
Expand using the FOIL Method.
Step 3.5.4.1
Apply the distributive property.
Step 3.5.4.2
Apply the distributive property.
Step 3.5.4.3
Apply the distributive property.
Step 3.5.5
Simplify and combine like terms.
Step 3.5.5.1
Simplify each term.
Step 3.5.5.1.1
Cancel the common factor of .
Step 3.5.5.1.1.1
Move the leading negative in into the numerator.
Step 3.5.5.1.1.2
Factor out of .
Step 3.5.5.1.1.3
Cancel the common factor.
Step 3.5.5.1.1.4
Rewrite the expression.
Step 3.5.5.1.2
Move the negative in front of the fraction.
Step 3.5.5.1.3
Cancel the common factor of .
Step 3.5.5.1.3.1
Move the leading negative in into the numerator.
Step 3.5.5.1.3.2
Factor out of .
Step 3.5.5.1.3.3
Cancel the common factor.
Step 3.5.5.1.3.4
Rewrite the expression.
Step 3.5.5.1.4
Multiply by .
Step 3.5.5.1.5
Cancel the common factor of .
Step 3.5.5.1.5.1
Factor out of .
Step 3.5.5.1.5.2
Cancel the common factor.
Step 3.5.5.1.5.3
Rewrite the expression.
Step 3.5.5.1.6
Rewrite using the commutative property of multiplication.
Step 3.5.5.1.7
Multiply .
Step 3.5.5.1.7.1
Combine and .
Step 3.5.5.1.7.2
Multiply by .
Step 3.5.5.1.8
Cancel the common factor of .
Step 3.5.5.1.8.1
Factor out of .
Step 3.5.5.1.8.2
Cancel the common factor.
Step 3.5.5.1.8.3
Rewrite the expression.
Step 3.5.5.2
Combine the numerators over the common denominator.
Step 3.5.5.3
Add and .
Step 3.6
Combine the numerators over the common denominator.
Step 3.7
Add and .
Step 3.8
Add and .
Step 3.9
Subtract from .